Product Formula Research Articles

Similarity measure method of near-infrared spectrum combined with multi-attribute information

Due to the high-dimensionality, redundancy, and non-linearity of the near-infrared (NIR) spectra data, as well as the influence of attributes such as producing area and grade of the sample, which can all affect the similarity measure between samples. This paper proposed a t-distributed stochastic neighbor embedding algorithm based on Sinkhorn distance (St-SNE) combined with multi-attribute data information. Firstly, the Sinkhorn distance was introduced which can solve problems such as KL divergence asymmetry and sparse data distribution in high-dimensional space, thereby constructing probability distributions that make low-dimensional space similar to high-dimensional space. In addition, to address the impact of multi-attribute features of samples on similarity measure, a multi-attribute distance matrix was constructed using information entropy, and then combined with the numerical matrix of spectral data to obtain a mixed data matrix. In order to validate the effectiveness of the St-SNE algorithm, dimensionality reduction projection was performed on NIR spectral data and compared with PCA, LPP, and t-SNE algorithms. The results demonstrated that the St-SNE algorithm effectively distinguishes samples with different attribute information, and produced more distinct projection boundaries of sample category in low-dimensional space. Then we tested the classification performance of St-SNE for different attributes by using the tobacco and mango datasets, and compared it with LPP, t-SNE, UMAP, and Fisher t-SNE algorithms. The results showed that St-SNE algorithm had the highest classification accuracy for different attributes. Finally, we compared the results of searching the most similar sample with the target tobacco for cigarette formulas, and experiments showed that the St-SNE had the highest consistency with the recommendation of the experts than that of the other algorithms. It can provide strong support for the maintenance and design of the product formula.

Determinant evaluations inspired by Di Francesco's determinant for twenty-vertex configurations

In his work on the twenty vertex model, Di Francesco (2021) found a determinant formula for the number of configurations in a specific such model, and he conjectured a closed form product formula for the evaluation of this determinant. We prove this conjecture here. Moreover, we actually generalize this determinant evaluation to a one-parameter family of determinant evaluations, and we present many more determinant evaluations of similar type — some proved, some left open as conjectures.

Interaction mechanism and compatibility studies of silk protein peptide (SPP) with the common surfactants SDS and DTAB

The molecular interaction of low-molecular-weight SPP with common surfactants (SDS and DTAB) is a more complicated process than has been long believed. In this work, the interaction mechanism between SDS/DTAB and SPP was proposed using multiple methods including conductivity measurements, ST, UV-vis, FT-IR, DLS, fluorescence spectroscopy, and molecular docking simulations. Moreover, the foaming properties of the mixed systems were studied, and they were evaluated as cosmetics preservatives. The effects of various surfactant and protein concentrations and ratios on compatibility and functionality were studied. Based on the results, the mechanism of complex formation was identified as a cooperative van der Waals interaction followed by hydrophobic interaction and hydrogen bonding. A simpler head group leads to easier aggregation and interaction with the SPP, the formation of smaller-sized complexes, and a weaker impact on the fluorescence intensity. Thus, SDS monomers easily aggregate on SPP chains, leading to a stronger influence on the final secondary structure of SPP. This was confirmed by multiple spectroscopy methods. Comparing its single surfactant system, the SDS-SPP solution demonstrates better foaming power and the DTAB-SPP solution shows higher bacteriostatic activity. The good compatibility between SDS/DTAB and SPP can improve the functional properties of SDS or DTAB as well as lower the optimal concentration of each component. These results provide data and theoretical support for the design of cosmetic product formulas.

An Engineered Production Formula for Enhanced Artificial Stone Utilizing Stone Cutting Slurry and a Superplasticizer

The purpose of this paper is to demonstrate the technical feasibility of utilizing some of the local industrial waste (stone cutting wastewater and marble) in manufacturing artificial stone and enhancing its quality, with the addition of a superplasticizer (liquefier). The paper reviews the previous work and presents new experimental work. Artificial stone samples were casted according to two starting formulas obtained from local production facilities. Later on, an engineered production formula was developed and tested, based on product quality. The investigated experimental parameters included: compressive strength, water absorption, and workability of fresh concrete. The experimental results indicated that high compressive strength and a low water absorption for artificial stone is technically feasible. In term of the compressive strength of artificial stone the marble dust contributed better than limestone wastewater.

Doubling the order of approximation via the randomized product formula

Doubling the order of approximation via the randomized product formula

Some 𝑞-identities derived by the ordinary derivative operator

In this paper, we investigate applications of the ordinary derivative operator, instead of the q q -derivative operator, to the theory of q q -series. As main results, many new summation and transformation formulas are established which are closely related to some well-known formulas such as the q q -binomial theorem, Ramanujan’s 1 ψ 1 {}_1\psi _1 formula, the quintuple product identity, Gasper’s q q -Clausen product formula, and Rogers’ 6 ϕ 5 {}_6\phi _5 formula, etc. Among these results is a finite form of the Rogers-Ramanujan identity and a short way to Eisenstein’s theorem on Lambert series.

Towards Adiabatic Quantum Computing Using Compressed Quantum Circuits

We describe tensor network algorithms to optimize quantum circuits for adiabatic quantum computing. To suppress diabatic transitions, we include counterdiabatic driving in the optimization and utilize variational matrix product operators to represent adiabatic gauge potentials. Traditionally, Trotter product formulas are used to turn adiabatic time evolution into quantum circuits and the addition of counterdiabatic driving increases the circuit depth per time step. Instead, we classically optimize a parameterized quantum circuit of fixed depth to simultaneously capture adiabatic evolution together with counterdiabatic driving over many time steps. The methods are applied to the ground-state preparation of quantum Ising chains with transverse and longitudinal fields. We show that the classically optimized circuits can significantly outperform Trotter product formulas. Additionally, we discuss how the approach can be used for combinatorial optimization. Published by the American Physical Society 2024

A mixture design approach to develop new starter formulation for Lben: Key aroma compounds, physical, chemical and sensory properties of the product

The study investigated the evolution of the physicochemical and sensory properties of Lben fermented milk inoculated with different starter formulations. The aim was to determine the optimal starter culture formula for Lben production using different combinations of four strains, including three strains of Lactococcus lactis subsp. lactis with strain codes A, E and F and one strain of Leuconostoc mesenteroides subsp. mesenteroides with strain code C. While individual strains had previously demonstrated significant technological and organoleptic properties their interaction in mixtures had not been explored. In the study, a response surface methodology (mixture design approach) was applied to evaluate the effects of the interactions between strains on the physicochemical, antioxidant, volatile, and sensory properties of Lben, a fermented milk. In addition, product optimization using ridge analysis was performed to determine the ideal strain mixture formulation based on the sensory properties of Lben. The optimization goal for odor, taste, consistency, and overall preference was set to maximize their values. A high desirability score of 0.832 was achieved with the following percentage distribution: 34.39% for L. lactis E, 42.38% for L. lactis A, 10% for L. lactis F, and 13.23% for Leuc. mesenteroides C.

Homology and K-theory of dynamical systems IV. Further structural results on groupoid homology

Abstract We consider the homology theory of étale groupoids introduced by Crainic and Moerdijk [A homology theory for étale groupoids. J. Reine Angew. Math.521 (2000), 25–46], with particular interest to groupoids arising from topological dynamical systems. We prove a Künneth formula for products of groupoids and a Poincaré-duality type result for principal groupoids whose orbits are copies of an Euclidean space. We conclude with a few example computations for systems associated to nilpotent groups such as self-similar actions, and we generalize previous homological calculations by Burke and Putnam for systems which are analogues of solenoids arising from algebraic numbers. For the latter systems, we prove the HK conjecture, even when the resulting groupoid is not ample.

The Hartley–Bessel function: product formula and convolution structure

The Hartley–Bessel function: product formula and convolution structure

ALOCALIZEDBASEDAPPLICATIONFORAUTOMOBILEMECHANICSLOCATION-AWARESYSTEM

ALOCALIZEDBASEDAPPLICATIONFORAUTOMOBILEMECHANICSLOCATION-AWARESYSTEM

Riemann zeta functions for Krull monoids

The primary purpose of this paper is to generalize the classical Riemann zeta function to the setting of Krull monoids with torsion class groups. We provide a first study of the same generalization by extending Euler's classical product formula to the more general scenario of Krull monoids with torsion class groups. In doing so, the Decay Theorem is fundamental as it allows us to use strong atoms instead of primes to obtain a weaker version of the Fundamental Theorem of Arithmetic in the more general setting of Krull monoids with torsion class groups. Several related examples are exhibited throughout the paper, in particular, algebraic number fields for which the generalized Riemann zeta function specializes to the Dedekind zeta function.

Electrochemically Driven Transformation of Olivine LiFePO4 to Olivine NaFePO4 in Cells with Sodium Anode and Carbonate Electrolyte

AbstractThe direct electrochemical transformation of commercial LiFePO4 to NaxFePO4 olivine in a Na||LiFePO4 electrochemical cell with sodium electrolyte has been studied. Electrolytes containing 1 M of NaClO4 in ethylene carbonate (EC), dimethyl carbonate (DMC) and fluoroethylene carbonate (FEC) have been probed, and in the solvents with the ratio of EC:DMC:FEC=0.4:0.5:0.1 by volume, maximal values of the specific capacity (113 mAh g−1) with good cycling stability and maximal discharge currents are achieved upon sodiation. To determine the composition of the cathode material and utilization factor of LiFePO4, the dependence of open circuit voltage on specific capacity has been investigated. The general formula of the sodiation product can be written as Na0.88FePO4. Its theoretic specific capacity may be estimated as 135 mAh g−1. The composition of the products obtained is supported by XRD analysis, which suggests that in discharged cathodes, Coulombic influence of LiFePO4 crystallites on neighboring NaxFePO4 crystallites may enlarge the unit cell of the former and reduce its size of the latter. Probably, shrinkage in the presence of LiFePO4 stabilizes the olivine structure of NaxFePO4 and prevents its transformation from electrochemically active olivine to inactive maricite.

Some Orthogonal Combinations of Legendre Polynomials

The principle objective of this article is to introduce and investigate a type of orthogonal polynomials that are written as combinations of Legendre polynomials. This kind of polynomials can be viewed as generalized Jacobi polynomials (GJPs), since they are written in terms of Jacobi polynomials (JPs) with certain negative parameters. The analytic and inversion formulas of these polynomials are established. New derivative expressions for these polynomials are derived in detail in terms of their original polynomials. Other derivative expressions for these polynomials are found but in terms of some orthogonal and non-orthogonal polynomials. Some product formulas with some other polynomials are also obtained. Certain definite and weighted definite integrals are obtained using the newly introduced connection and product formulas.

Exploring the communication strategies in baby food supply: Differences between online and retail sales of baby milk

ABSTRACT The aim of this paper is to evaluate the variety and depth of the infant formula of milk products (IMP) assortment within the category of baby food comparing two different distribution channels. The marketing mix variables and communication strategies of 3066 references of IMP portfolio were collected directly in-store of large retail chain in the North-West of Italy and on the websites of the major baby food producers. Differences in the assortment composition were determined by considering two product lines, powdered and reconstituted milk (liquid), as well as considering milk categories according to their specialties, origin, packaging, and claims communicated on the product packaging. The results show heterogeneity in the assortment composition of IMP between the two considered channels, which differ in terms of product types and prices. The online channel focuses mainly on satisfying specific consumer needs through the offer of high value-added products. The IMP’ assortment planning is oriented to the exaltation of product nutritional value and safety, to the detriment of quality certifications and product’s origin communication. This research provides concrete tools to managers to improve the IMP planning and communication strategies for a successful sales policy.

Applications of Life Cycle Assessment in the Chocolate Industry: A State-of-the-Art Analysis Based on Systematic Review.

Chocolate is a popular food for its unique flavor and taste, rich nutritional value, and the psychological values brought to people. The raw material production of chocolate, product manufacturing, sales and transportation have different degrees of environmental impact. This review explores the environmental hot spots in the life cycle of chocolate and puts forward corresponding suggestions for the improvement. By applying a systematic review method, this paper collected 25 articles on life cycle assessment (LCA) of the environmental impact of the chocolate industry. It is found that the life cycle of chocolate has the highest environmental impact in the raw material production and chocolate manufacturing stages (accounting for 77-97% of total impacts), among which milk powder, sugar and cocoa derivatives are the important contributors to significant environmental burden. Dark chocolate generates the lowest carbon emissions (1.67 kg CO2 eq/kg product) among existing chocolate categories, while the chocolate confectionery products release the highest carbon emissions (6.76 kg CO2 eq/kg product) among chocolate-containing products. Improvement measures are proposed for reducing environmental impacts and for selecting environmentally friendly product formulae. This study can provide benchmarking for the chocolate industry and improves the understanding of life cycle environmental impacts of chocolate products.

Effect of Chemical and Granular Organic Fertilizer with Hormone Mixed Formula (HO) for Quality And Productivity on Hoary Basil (Ocimum Americanum L.)

Purpose: This research study aimed to develop chemical and granular organic fertilizers with hormone mixed formula (HO) and examine its effect on growth, productivity and active principles of hoary basil (Ocimum americanum L.) and the effect of HO fertilizer on soil properties. Method: Experiments were conducted in an RCBD with 6 treatments 4 replications on 1.2x4 m plots with 32 seedlings on each. The soil properties before and after experiments, growth rate, yield and active principles were analyzed by ANOVA, and compared by a DMRT method at the reliability of 95%. The experiments were conducted between September 2020 and September 2021. Results and Conclusion: The results showed that the HO fertilizers (T4, T5 and T6) improved organic matter, the soil pH, bulk density, soil porosity and water holding capacity. The HO fertilizers also significantly increased secondary and micronutrients. The plants with the HO fertilizers, especially with T6 and T5, showed the highest growth in terms of height, stem size, number of branches and canopy size, with statistically significant differences compared to the other treatments. In terms of yield productivity, T6 had the highest yield (3,192.7), followed by T2 (2,920.5), T5 (2,728.8), T4 (2,667.7), T3(1,952.1) and T1(1,735.8 kg/rai.). According to the active principle analysis, eugenol and methyl eugenol were found highest under T6 (HO-3). As for the net profit in hoary basil production, T6 showed the highest profit of 94,965 baht/rai. Implications of the Research: It was concluded that the HO fertilizers, as environmentally friendly fertilizing options, could sustainably improve soil quality and HO-3, in particular, has proved to be suitable for hoary basil production to provide high quality, safe products for both domestic and international markets. Originality/Value: This study highlights the effectiveness of HO fertilizers on increasing yields, yield component and active principles of hoary basil.

THE JARROW AND TURNBULL SETTING REVISITED

We consider a financial market with zero-coupon bonds that are exposed to credit and liquidity risk. We revisit the famous Jarrow & Turnbull (1995) setting in order to account for these two intricately intertwined risk types. We utilize the foreign exchange analogy that interprets defaultable zero-coupon bonds as a conversion of nondefaultable foreign counterparts. The relevant exchange rate is only partially observable in the market filtration, which leads us naturally to an application of the concept of platonic financial markets as introduced by Cuchiero et al. (2020). We provide an example of tractable term structure models that are driven by a two-dimensional affine jump diffusion. Furthermore, we derive explicit valuation formulae for marketable products, e.g. for credit default swaps.

Skew-convex function rings and evaluation of skew rational functions

The product formula for evaluating products of skew polynomials is used to construct a class of rings. As an application, we present a method of evaluating quotients of skew polynomials.

A comprehensive review on effective parameters on microalgae productivity and carbon capture rate

Rising carbon emissions caused by population growth and industrialization is a significant environmental challenge in various countries. To combat this issue, Renewable Energy (RE) and Carbon Capture and Storage (CCS) technologies should be commercialized to reduce Greenhouse Gas (GHG) emissions and generate carbon-free energy. One such technology is the use of microalgae, which can directly capture CO2 from the air through photosynthesis and potentially produce biofuels due to their high energy content. However, the carbon capture rate of microalgae varies globally due to numerous parameters and variables affecting microalgae productivity. Additionally, microalgae productivity and carbon capture formulas yield different results worldwide, especially in outdoor industrial-scale cultivation. This research aims to comprehensively review the effective variables and parameters in carbon capture by microalgae based on microalgae productivity and carbon capture formulas. The research also ranked countries based on CO2 production in four different categories to determine whether the biggest carbon producer countries could exhibit suitable weather conditions for microalgae cultivation. Findings reveal optimal ranges of critical variables in the microalgae growth formula, including temperature, solar radiation intensity, Photon Flux Density (PFD), and sunlight duration. The study also analyzes microalgae cultivation, carbon capture, and oxygen production formula in different systems such as Open Ponds (OP), Tubular Photobioreactors (TPBR), and Flat Plate Photobioreactors (FPPBR), while discussing other influential parameters. In conclusion, emphasizing the adjustment and utilization of optimal values of effective parameters in microalgae cultivation not only holds promise for future carbon capture by microalgae but also pushes human beings toward sustainable development goals.